This is the third competitive renewal of a grant to develop methods to study the genetic epidemiology of common disease. The current proposal will test, quantify, and expand findings of the last grant period, findings that include: 1) demonstrating that if a disease is determined by two epistatically interacting loci, one of which is linked to a marker, the effect of the second locus on linkage analysis can be subsumed under 'reduced penetrance' with little loss of power in the linkage results; 2) demonstrating the effect of family sampling schemes on heterogeneity in linkage data; 3) quantifying the amount of linkage information necessary to infer the correct mode of inheritance from linkage data; 4) showing how there can be association between a disease and a marker but no linkage, and that this can be explained by the existence of a susceptibility locus as opposed to a 'necessary' locus; and 5) developing a test to distinguish between 'necessary' and 'susceptibility' loci. In this proposal, the investigators continue to use both analytic and computer simulation methods to develop new ways of looking at inheritance in disease populations and apply the new methods to disease data. There are five main areas of investigation, as follow: 1) test whether lod score methods or non-parametric methods are best for analyzing affected sib pair data; 2) apply the MMLS (or mod score) method to intermediate models and to additive models of inheritance; 3) determine the type I error for the MMLS method; 4) expand the partitioned-linkage association (PAL) test to distinguish the susceptibility locus hypothesis from the linkage disequilibrium plus heterogeneity hypothesis; and 5) use simulation techniques to determine the bias in estimating genetic parameters in linkage data because of proband dependent sampling, and to develop approximate simulation solutions for ascertainment bias correction. The population genetic characteristics of relatively common diseases such as diabetes, epilepsy, thyroid disease, etc., remain obscure, in part because the genetic analysis methodology available to study disease populations has proven inadequate. The investigators state that the work proposed here will, as with past work, expand the repertoire of methods used to study genetic disease.